Not if its defined as a const you can't. Its a scoping issue, if you don't include the self:: or DB:: it doesn't know what you're looking for. Although its also a constant, its not a defined constant like the define() function which places it into a global scope.
If you really wanted it to, you should be able to use the value of a constant as a constant. I believe it only needs to be constant data (ie: not a variable), so you may be able to do this: